# Product Spaces!

• 04-13-2012, 01:23 PM
h2oskidude
Product Spaces!

P5 is an innerproduct space with an inner product. We applied the Gram Schmidt process tot he basis {1,x,x^2,x^3,x^4} and obtained the following as the result {f1,f2,f3,f4,x^4+2}.
a. What is the orthogonal complement of P3 in P5 with erspect to this inner product?
b. What is the length of 2f1 + f3 -f4?

Do we reverse the Gram Schmidt process somehow? I'm not even sure that its possible
• 04-14-2012, 01:08 PM
HallsofIvy
Quote:

Originally Posted by h2oskidude

P5 is an innerproduct space with an inner product. We applied the Gram Schmidt process tot he basis {1,x,x^2,x^3,x^4} and obtained the following as the result {f1,f2,f3,f4,x^4+2}.
a. What is the orthogonal complement of P3 in P5 with erspect to this inner product?
b. What is the length of 2f1 + f3 -f4?

Do we reverse the Gram Schmidt process somehow? I'm not even sure that its possible

There is no way to do this problem without knowing what the inner product is.

By the way, the term "product space" usually applies to the Cartesian product of two "spaces". It does not usually mean "inner product spaces".